SUMMARYThis paper presents an augmentation method that enables bilinear finite elements to efficiently and accurately account for arbitrary, multiple intra‐elemental discontinuities in 2D solids. The augmented finite element method (A‐FEM) employs four internal nodes to account for the crack displacements due to an intra‐elemental weak or strong discontinuity, and it permits repeated elemental augmentation to include multiple interactive cracks. It thus enables a unified treatment of damage evolution from a weak discontinuity to a strong discontinuity, and to multiple interactive cohesive cracks, all within a single bilinear element that employs standard external nodal DoFs only. A novel elemental condensation procedure has been developed to solve the internal nodal DoFs as functions of the external nodal DoFs for any irreversible, piece‐wise linear cohesive laws. It leads to a fully condensed elemental equilibrium equation with mathematical exactness, eliminating the need for nonlinear equilibrium iterations at elemental level. The new A‐FEM's high‐fidelity simulation capabilities to interactive cohesive crack formation and propagation in homogeneous, and heterogeneous solids have been demonstrated through several challenging numerical examples. It is shown that the proposed A‐FEM, empowered by the new elemental condensation procedure, is numerically very efficient, accurate, and robust. Copyright © 2014 John Wiley & Sons, Ltd.

This paper presents a new augmented finite element method (A-EEM) that can account for path-arbitrary, multiple intraelemental discontinuities with a demonstrated improvement in numerical efficiency by two orders of magnitude when compared to the extended finite element method {X-EEM). We show that the new formulation enables the derivation of explicit, fully condensed elemental equilibrium equations that are mathematically exact within the finite element context. More importantly, it allows for repeated elemental augmentation to include multiple interactive cracks within a single element without additional external nodes or degrees of freedom (DoEs). A novel algorithm that can rapidly and accurately solve the nonlinear equilibrium equations at the elemental level has also been developed for cohesive cracks with piecewise linear traction-separation laws. This efficient new solving algorithm, coupled with the mathematically exact elemental equilibrium equation, leads to dramatic improvement in numerical accuracy, efficiency, and stability when dealing with arbitrary cracking problems. The A-EEM's excellent capability in high-fidelity simulation of interactive cohesive cracks in homogeneous and heterogeneous solids has been demonstrated through several numerical examples.

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